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arXiv · 2305.08748

Monodromy of double elliptic logarithms

Francesco Tropeano
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Abstract

We determine the relative monodromy group of abelian logarithms with respect to periods in the cases of fibered products of elliptic schemes. This gives rise to a result stronger than a theorem due to Y. André and implies in particular the algebraic independence of the logarithm of any non-torsion section and the periods. We then conjecture an analogous result for the general case of an abelian scheme of arbitrary relative dimension. This generalizes a theorem of Corvaja and Zannier which determines the said group in the case of a single elliptic scheme.

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Francesco Tropeano. 2023-05-15. Monodromy of double elliptic logarithms. https://arxiv.org/abs/2305.08748

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